On the Pohozaev identity for the fractional $p$-Laplacian operator in $\mathbb{R}^N$

Vincenzo Ambrosio

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arXiv · 2301.06537

On the Pohozaev identity for the fractional $p$-Laplacian operator in $\mathbb{R}^N$

Vincenzo Ambrosio

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Abstract

In this paper, we show the existence of a nontrivial weak solution for a nonlinear problem involving the fractional $p$-Laplacian operator and a Berestycki-Lions type nonlinearity. This solution satisfies a Pohozaev identity. Moreover, we prove that any sufficiently smooth solution fulfills the Pohozaev identity.

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Vincenzo Ambrosio. 2023-01-16. On the Pohozaev identity for the fractional $p$-Laplacian operator in $\mathbb{R}^N$. https://arxiv.org/abs/2301.06537

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